On a continuum thermodynamics formulation and computational aspects of finite growth in soft tissues

Abstract

In this paper, we try to settle the bases of a concise modelling of growth within the unified framework of continuum thermodynamics. Special emphasis is placed on the modelling of soft biological tissues at finite strains. For this, we adopt the nowadays well-known kinematic assumption of a multiplicative decomposition of the deformation gradient into an elastic part and a growth part. It is shown how continuum thermodynamics is crucial in setting convenient forms for the coupling between stress and growth in general. The particularization to isotropy simplifies considerably the growth modelling from both the theoretical and the numerical points of view. Simple growth constitutive equations are proposed and embedded into a finite element context. Finally, representative numerical examples examining stress-dependent growth and residual stress arising from growth and resorption close this study. © 2011 John Wiley & Sons, Ltd.